In mean computation from histogram topic , what happen if we consider a interval which has more frequency with almost same value

Example - In Sachin’s score data 10-20 interval has 59 frequency

If all 59 occurrences has value as either 11 or 19 then there will be high difference between approximate sum and actual sum

Actual sum [ when all 11] - 649

Actual sum [ when all 19] - 1121

Approximate sum [ 14.5 * 59] - 855.5

Kindly explain if this is special scenario to be handled in different approach.